so-called static and rotary derivatives. These are nothing more than the coefficients in the 

 equations of motion. Having this information, reliance can be placed on the coefficients, and 

 the comparison between theoretical and experimental motions then becomes an adequate test 

 of the linear equations. In the past, no thorough experimental study of this kind has been 

 made on ship forms. 



In this report only the first (jiase of a broader investigation will be described; namely, 

 the forces and moments due to heaving motions. It is the purpose of the overall study to 

 completely define the terms in the equations by experimental means, to evaluate the existing 

 analytical procedures for determining these terms, and finally, to compare predicted and ob- 

 served motions using these experimental results. 



It has been most common in the past to use a free oscillation technique for such studies 

 primarily due to its simplicity. However, there are difficulties in interpreting the data since 

 the motion is not strictly periodic. Also, we are not assured of a given frequency of oscil- 

 lation and, of course, the effect of amplitude cannot be determined. 



The forced oscillation of the model overcomes these objections, with two alternative 

 methods being possible. Either the model can be supported on a spring and oscillated, or it 

 can be oscillated while supported on a stiff force balance. The latter method has been used 

 because the amplitude of oscillation can be preset and the coupling forces and harmonic con- 

 tent can be directly measured. 



At the outset, credit should be given Dr. Georg Weinblum for having led the way in in- 

 vestigations of this kind. It was through his efforts while associated with the David Taylor 

 Model Basin several years ago that the Model Basin now possesses the mechanical oscil- 

 lator, as well as the ship models used for these tests. 



THE MODEL 



The symmetrical model used in the present tests was one of a family constructed to 

 mathematical lines defined by Weinblum.^ The family has the general form 



where the longitudinal, transverse, and vertical offsets of the hull, x, y, and s, are divided 

 by the half-length, half-breadth, and draft to yield the nondimensional offsets, f, 77, and ^. 

 The equation of the waterplane is r^ = X{^) and the equation of the midship section is 

 T] = Z{C)- For the particular model used the form was described by 



,, = [(1 - ^2) _ (^2 _ ^) ^10] [1 _ 0.3^8 - 0.7C'5°] 

 The model constants are tabulated in Table 1 and the body plan is shown in Figure 1. 



References are listed on page 31, 



